The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is

Options

A. 2
B. `1//2`
C. 4
D. 16

Answer

A

Explanation

Intensity (I) = `4I_(0) cos^(2)(phi)/(2)`
At central position, `I_(1)= 4I_(0)`
`Deltaphi= 2pi xx (1)/(4) = (pi)/(2)` radian
`I_(2)= 4I_(0) cos^(2)((pi)/(4))= 2I_(0)`
`:. (I_(1))/(I_(2))= (4I_(0))/(2I_(0))= 2`